The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for image reconstruction using parallel MRI techniques.
Methods for acceleration of magnetic resonance image acquisition were introduced about a decade ago. Broadly stated, these are techniques which allow for the number of phase encoding measurements or “views” necessary for MR image formation to be reduced compared to some reference number. This is done by sampling along the phase encoding direction more coarsely than is normally required to generate an image with a given field-of-view (“FOV”) and spatial resolution. The undersampling is accounted for in some manner by using measurements from multiple receiver coils. There are two classes of acceleration techniques: those based in k-space and those based in image-space.
Techniques based in k-space include SMASH and GRAPPA. For view locations at which measurements are not made directly, measurements at those locations are estimated using actual measurements made at nearby view locations in k-space. The estimation function or “kernel” used is itself created from fully sampled acquisition performed at and about the k-space origin. This is called the “training region.” The fully sampled data in the training region are used to model how measurements at target view locations can be estimated from nearby views for which the data are measured. With k-space-based methods the degree of undersampling that is typically done is an integer. That is, away from the fully sampled training region only every other or every third or fourth view is actually measured. This results in a nominal acceleration, R, which is constrained to being an integer: R=2, 3, 4, etc. Because the training region is fully sampled, the nominal acceleration is not attained over the entirety of k-space. Consequently, the net acceleration is reduced somewhat, typically 10% to 20%, from the nominal.
Image-based acceleration is performed differently. In any MRI acquisition the increment Δk between sampled positions along a direction in k-space is established by the FOV along that direction in an inverse relationship: Δk=1/FOV. For standard, non-accelerated acquisition the FOV used is set to comfortably encompass the object. For image-based acceleration methods the k-space sampling interval is intentionally chosen as if the FOV were smaller than the object dimension by the acceleration factor, R. Due to the inverse relationship this causes the k-space increment to be larger than normal. This in turn allows the time required to sample out to some maximum k-value to be reduced because the increment is larger. However, the reduced field-of-view, FOV/R, causes foldover or aliasing of the image onto itself. Using data acquired simultaneously from multiple receiver coils, the aliased images from the multiple coils can be algebraically unfolded into a normal-appearing unaliased image.
The use of acceleration methods to reduce the acquisition time for a given spatial resolution carries with it a penalty, the penalty being a reduction in the signal-to-noise ratio (SNR) of the accelerated image vs. that in an unaccelerated reference image. In general, as acceleration R is increased, the SNR decreases. The degree of SNR penalty is related to the interplay of the spatial response functions or “sensitivity maps” of the individual receiver coils across the object. These sensitivity maps are generally measured as part of the process of performing accelerated acquisition. Importantly, the degree of SNR loss in the accelerated image can be calculated from the sensitivity maps. This calculation results in what is called the “g-factor.” That is, it is not necessary to perform an accelerated scan to determine what the relative SNR loss is in the images formed from that scan.
An aspect of image-based acceleration relevant to this disclosure is that the k-space increment need not be an integer multiple of the standard increment 1/FOV. That is, Δk=R/FOV, where R can be an arbitrary number larger than unity. Equivalently, the FOV can be progressively reduced from its starting value, and with greater reduction the degree of aliasing increases. This can be valuable in image-based vs. k-space-based acceleration. For k-space-based methods if, for example, the SNR loss with a nominal acceleration of R=2 is acceptable but for R=3 it is unacceptable, then it would be necessary to use R=2. However, for the image-based approach although R=3 may be unacceptable, it is possible that R=2.8, for example, would still have adequate SNR, thereby allowing an acceleration 2.8/2.0 or 40% higher than that allowed with the k-space-based approach.
In image-based acceleration it is useful to know if specific regions within the full, unreduced FOV are known to have zero signal. Such regions occur, for example, in the air outside the object but still within the square or rectangular FOV used in image acquisition. From this information one can force the signal in these regions to be zero in the unfolding process. This then reduces the uncertainty in the unfolding process, for example by preventing measured aliased signal from being assigned to points known to have zero signal. This process of identifying regions within the FOV but outside the object and known to have zero signal is called “masking.”
The discussion thus far about acceleration has made no distinction as to how many directions the acceleration is being performed along. For 2DFT image acquisition, acceleration R can be done along the one phase encoding direction, Y. For 3DFT acquisition, it is possible to perform acceleration separately along two phase encoding directions, Y and Z. The respective accelerations can be called RY and RZ. The overall acceleration R is equal to the product of the individual Y and Z accelerations, R=RY×RZ.